A clamp structure with an improved spring action is described in my prior U.S. Pat. No. 5,138,747 which disclosed an auxiliary spring for interconnecting overlapping band portions. In this patent, the mutually facing end portions of the leaf spring members forming the auxiliary spring terminated in end portions bent to point in the direction toward the top portions of the leaf spring members while the connection with the inner and outer band portions took place by means of substantially S-shaped hooks adapted to engage in the apertures provided in the inner end portions. As the strength of the hooks bent out of the band portions depended at least to a large extent on the clamping band material, such as the thickness thereof, a limit exists in practice for the maximum spring force which this connection can withstand before there is danger of disengagement. Additionally, the extent of relative movement of the inner and outer band portions and therewith the extent to which the auxiliary spring can be subjected to stretching forces was limited by a hook extending outwardly and adapted to engage in an oversized aperture. Though the limiting action proved reasonably successful, the outwardly extending hook was not able to provide a completely satisfactory guide function to keep the inner and outer band portions in proper mutual overlapping alignment.